There is a conjecture that all possible sequences of digits appear in pi. IIRC, this is true for almost all real numbers, but no-one knows how to prove (or disprove) it for pi.
Right. But say at the quadrillionth decimal place you find a sequence of a million zeros, then a million ones, then a sequence of ones and zeros that forms a recognizable picture when plotted as a bitmap. Even though you'd expect that sequence to appear *somewhere* in pi, the odds against it occuring so early by "chance" would be astronomical.